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dc.contributor.advisorDennis Auroux.en_US
dc.contributor.authorPascaleff, James Thomasen_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2011-12-19T19:00:46Z
dc.date.available2011-12-19T19:00:46Z
dc.date.copyright2011en_US
dc.date.issued2011en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/67812
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 115-117).en_US
dc.description.abstractWe construct a family of Lagrangian submanifolds in the Landau-Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the twisting sheaf 0(1), and hence their Floer cohomology groups form an algebra isomorphic to the homogeneous coordinate ring. An interesting feature is the presence of a singular torus fibration on the mirror, of which the Lagrangians are sections. This gives rise to a distinguished basis of the Floer cohomology and the homogeneous coordinate ring parameterized by fractional integral points in the singular affine structure on the base of the torus fibration. The algebra structure on the Floer cohomology is computed using the symplectic techniques of Lefschetz fibrations and the TQFT counting sections of such fibrations. We also show that our results agree with the tropical analog proposed by Abouzaid-Gross-Siebert. Extensions to a restricted class of singular affine manifolds and to mirrors of the complements of components of the anticanonical divisor are discussed.en_US
dc.description.statementofresponsibilityby James Thomas Pascaleff.en_US
dc.format.extent117 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleFloer cohomology in the mirror of the projective plane and a binodal cubic curveen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc767908243en_US


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